Question

Please help, i’ll give brainiest answer :) [Image]

Answer 1

Answer: 20

Step-by-step explanation:

• Step 1: Find the vertices (intersections) of the constraints by either graphing or solving the system of equations. I graphed them and found two of the vertices: (0, 1) and (4,0) but needed to solve the system to find the third vertex (point of intersection).

-x + 3 = $\frac{1}{3}x$ + 1

+x   -1     +x  -1

      2 = $\frac{4}{3}x$

  (3)2 = $(3)\frac{4}{3}x$

      6 = 4x

   ÷4   ÷4

     $\frac{3}{2}$ =  x

y = $\frac{1}{3}x$ + 1

  = $\frac{1}{3}(\frac{3}{2)}$ + 1

  =  $\frac{1}{2}$ + 1

   = $\frac{3}{2}x$

Third vertex is at $(\frac{3}{2},\frac{3}{2)}$

• Step 2: Input the vertices into the objective function: C = 5x - 4y

(0, 1): C = 5(0) - 4(1)

            =   0   -  4

            =      -4

$(\frac{3}{2},\frac{3}{2)}$: C = 5$(\frac{3}{2})$ - 4$(\frac{3}{2})$

            = $\frac{15}{2}$ - $\frac{12}{2}$

            =      $\frac{3}{2}$

            =      1.5

(4, 0): C = 5(4) - 4(0)

            =  20   -  0

            =      20

• Step 3: Evaluate the answers above to find the maximum: 20